User blog:GalacticAttorney/Calc Time Boyz: KE of Muffin Knight's Arrows (and other stuff)
Eyy b0ss So this is my first time doing this sort of thing. Feel free to point out any mistakes I may have made in calculating. Speed of Muffin Knight's Arrows To start off, we'll say Muffin Knight is the height of an average 10 year-old boy (as he is just a child) for this, which puts him at 4'10". It takes .47 seconds for a single arrow to travel across the entire Bridge stage, which, using Muffin Knight's height to scale width, is approximately 15 Muffin Knights long. Keep in mind that height is consistent across every form, so using the Unicorn's height for this doesn't change the results. So, that means the arrow is travelling 72.45 feet (15 x 4.83 ft) in a timespan of .47 seconds. So, divide 72.45 by .47, and (accounting for significant figures) we get a speed of approximately 154.1 feet per second. Drop that into a conversion calculation and 154.1 feet per second translates to 105.1 miles per hour. So, yeah, 100 mph arrows. Slower than the average arrow, but when it's a 10 year old firing it you can't really expect much. XP Now for calculating the kinetic energy. To do this we need the weight of a singular arrow. One arrow is approximately half of Muffin Knight's height, so about 2'5" in length for a single arrow. Several factors need to be taken into account here. 1. The arrows are all entirely constructed of the same material 2. The arrows seem to shine in the light when fired, not just at the arrowtip either 3. The color of the arrows is a sort of tannish brown So, the fact that the entire arrows shines eliminates the fact that it could be made of wood. This means that it's probably composed entirely of a metal. Add in the fact that they are a tannish brown, and (I think, I could be incorrect) the arrows would probably be composed entirely of copper. Copper's molar mass is 63.56 g/mol and the volume of a single mole is approximately 8 mL. Using a cylinder volume calculator, we can put the average radius of an arrow shaft (.625 inches, since modern-day arrowheads are required to be at least 1.25 inches wide and they are designed to be the same width as the shaft) and the length of the arrow (2.42 ft) into the equation to get a volume of 584.03 mL for each individual arrow. Next we take the volume we just found and divide it by the number of mL in a mole of copper. Simple: 584.03 / 8 = 68.503 moles of copper in a single arrow. Now we multiply that by the molar mass of copper and, for the final weight of one arrow, we get 4354.1 grams. That translates to 9.599 pounds per arrow. And to calculate the kinetic energy of a single arrow, we need the weight to be in grains. 9.599 grams converts to a whopping 67192.907 grains. Finally, put the grains of one arrow and the speed of an arrow into a kinetic energy calculator, and the final result is... Kinetic Energy of one arrow: 3539.5235046066327 Joules. One arrow is Street +, nice. Well, this was a long-ass first calc. Maybe I'll do more. Idk. If I feel like it. Category:Blog posts